Creep events and creep noise in gravitational-wave interferometers: basic formalism and stationary limit

Abstract

In gravitational-wave interferometers, test masses are suspended on thin fibers which experience considerable tension stress. Sudden microscopic stress release in a suspension fiber, which I call a 'creep event', would excite motion of the test mass that would be coupled to the interferometer's readout. The random test-mass motion due to a time-sequence of creep events is referred to as 'creep noise'. In this paper I present an elasto-dynamic calculation for the test-mass motion due to a creep event. I show that within a simple suspension model, the main coupling to the optical readout occurs via a combination of a "dc" horizontal displacement of the test mass, and excitation of the violin and pendulum modes, and not, as was thought previously, via lengthening of the fiber. When the creep events occur sufficiently frequently and their statistics is time-independent, the creep noise can be well-approximated by a stationary Gaussian random process. I derive the functional form of the creep noise spectral density in this limit, with the restrictive assumption that the creep events are statistically independent from each other.